The comparators are connected to create window comparators. This configuration will output a digital 1 if the input is between two reference voltages, and 0 if it is not. Using this, the analog output of the IR range sensor can be converted to digital values.

The 555 timer takes care of creating the output waveform. A specific resistor is switched in to the timer’s RC circuit depending on which window comparator is active. This allows for a different tone to be played depending on the distance from the IR sensor.

The result is a square wave, which has a frequency dependant on how close an object is to the IR sensor. By selecting the right resistances for each distance, the theremin can be tuned to play a specific scale.

This is a neat project for people looking to learn digital electronics, and the write up does a great job of explaining the theory. After the break, check out a video of the theremin generating some tones.

The purpose of this project is to teach electronics, therefore it is complicated by design with the intent of letting the user understand various circuits and their tasks.
Remember: when you’re doing something for learning, the journey is the reward.
A single 8 pin microcontroller could easily read the output of a couple of these sensors like a real theremin (amplitude and frequency), generate a real sine wave by reading a lookup table in memory and producing MIDI output for external sound generators. That would be nicer, but its teaching value in analog electronics would also be vastly inferior.

Variability is the defining action of a Theremin. Not discrete steps. Air keyboard is more descriptive.
Remember; do not mix different cells in your device, I see frowns and smiles mixed in that holder. Anyone starting in electronics should start with a power supply project.